My best was 10 in a row. But as my opponents got better obviously that streak ended. The latest winning streak was 7 wins in a row, from decent opponents with a loss in between from a player that cheated apparently.

I've had many long winning streaks, but when you do random seeks of any rating, you get many people accepting that are 3-400 points lower, so it's probably typical for most players over 1600 to have long winning streaks.